Elliptic systems of variable order

Thomas Krainer, Gerardo A. Mendoza

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The general theory of boundary value problems for linear elliptic wedge operators (on smooth manifolds with boundary) leads naturally, even in the scalar case, to the need to consider vector bundles over the boundary together with general smooth fiberwise multiplicative group actions. These actions, essentially trivial (and therefore invisible) in the case of regular boundary value problems, are intimately connected with what passes for Poisson and trace operators, and to pseudodifferential boundary conditions in the more general situation. Here the part of the theory pertaining to pseudodifferential operators is presented in its entirety. The symbols for these are defined with the aid of an intertwining of the actions. Also presented here are the ancillary Sobolev spaces, an index theorem for the elliptic elements of the pseudodifferential calculus, and essential ingredients for analyzing boundary conditions of Atiyah-Patodi-Singer type in the more general theory.

Original languageEnglish (US)
Pages (from-to)127-160
Number of pages34
JournalRevista Matematica Iberoamericana
Volume31
Issue number1
DOIs
StatePublished - Jan 1 2015

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Elliptic Systems
Boundary Value Problem
Boundary conditions
Index Theorem
Michael Francis Atiyah
Manifolds with Boundary
Smooth Manifold
Pseudodifferential Operators
Group Action
Operator
Wedge
Vector Bundle
Sobolev Spaces
Multiplicative
Siméon Denis Poisson
Trivial
Calculus
Trace
Scalar

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Krainer, Thomas ; Mendoza, Gerardo A. / Elliptic systems of variable order. In: Revista Matematica Iberoamericana. 2015 ; Vol. 31, No. 1. pp. 127-160.
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Elliptic systems of variable order. / Krainer, Thomas; Mendoza, Gerardo A.

In: Revista Matematica Iberoamericana, Vol. 31, No. 1, 01.01.2015, p. 127-160.

Research output: Contribution to journalArticle

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